Maths-
General
Easy

Question


For the linear function h, the table above shows several values of x and their corresponding values of h(x). Which of the following defines h ?

  1. straight h left parenthesis straight x right parenthesis equals 2 straight x minus 3
  2. straight h left parenthesis straight x right parenthesis equals 3 straight x minus 5
  3. straight h left parenthesis straight x right parenthesis equals 4 straight x minus 7
  4. straight h left parenthesis straight x right parenthesis equals 4 straight x minus 9

The correct answer is: straight h left parenthesis straight x right parenthesis equals 3 straight x minus 5


    HINT :- Assume ,let the equation h (x) be in the form ax + b as it is a linear function. Substitute the values in the table and get equations to get the values of a and b . Now, substitute them in the assumed equation ax + b.
    let the equation h(x) be in the form ax + b as it is a linear function

    Step 1 :  Substitute the values in the table and get equations .
    ax + b = h(x) let x =2 and h(2) = 1 From the above table.
    2a + b = 1 — equation 1.
    let x = 4 and h (4)  = 7  From the above table.
    4a + b = 7 — equation 2.
    Step 2: solving equations to get a
    Equation 2 - equation 1 we get the following
    4a + b - 2a - b = 7 - 1
    not stretchy rightwards double arrow 2 straight a space equals space 6
not stretchy rightwards double arrow straight a space equals space 3
    Step 3:- solving equations to get b.
    Substitute the value a= 3 in the equation 1 to get b .
    2 space left parenthesis 3 right parenthesis space plus space straight b space equals space 1 space not stretchy rightwards double arrow space straight b space equals space minus 5
not stretchy rightwards double arrow space straight b space equals space minus 5

    We get h(x) = 3x - 5 by substituting the values of a and b 

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